Bad experience with chess piece — not the king, the horse! (9)
I believe the answer is:
nightmare
'bad experience' is the definition.
'nightmare' can be an answer for 'experience' (I have seen 'Horrifying experience' mean 'nightmare' so perhaps 'experience' could also mean 'nightmare'). I'm unsure of the 'bad' bit.
'chess piece not the king the horse' is the wordplay.
'chess piece' becomes 'knight' (knight is a type of chess piece).
'not' suggests deleting specific letters.
'the king' becomes 'K' (chess abbreviation).
'the horse' becomes 'mare' (mare is a kind of horse).
'knight' with 'k' taken out is 'night'.
'night'+'mare'='NIGHTMARE'
'with' is the link.
Can you help me to learn more?
(Other definitions for nightmare that I've seen before include "Terrifying dream" , "Horrible experience" , "Awful experience" , "Horrifying experience" , "that might upset the rest" .)